/*
Generated by Allan Steel in Magma, 2010.

Field defining polynomial: x^4 - 3*x^2 + 4.

Traces:    [ 0, 0 ]
Density:   [ 0.99718750, 0.012500000 ]
Numer max: [ 64, 1 ]
Numer av:  [ 5.0308594, 0.0046875000 ]
Denom max: [ 96, 2 ], [ [ <2, 5>, <3, 1> ], [ <2, 1> ] ]
Denom LCM: [ 192, 2 ], [ [ <2, 6>, <3, 1> ], [ <2, 1> ] ]

Character:
( 80, -80, 0, -1, -80*zeta(28)_4, 80*zeta(28)_4, 0, 0, 0, 0, 0, 0, 0, 1, 
    -zeta(28)_7^4 - zeta(28)_7^2 - zeta(28)_7 - 1, zeta(28)_7^4 + zeta(28)_7^2 +
    zeta(28)_7, 0, 0, 0, 0, -zeta(28)_4, zeta(28)_4, -zeta(28)_7^4 - 
    zeta(28)_7^2 - zeta(28)_7, zeta(28)_7^4 + zeta(28)_7^2 + zeta(28)_7 + 1, 0, 
    0, 0, 0, -zeta(28)_4*zeta(28)_7^4 - zeta(28)_4*zeta(28)_7^2 - 
    zeta(28)_4*zeta(28)_7, zeta(28)_4*zeta(28)_7^4 + zeta(28)_4*zeta(28)_7^2 + 
    zeta(28)_4*zeta(28)_7, -zeta(28)_4*zeta(28)_7^4 - zeta(28)_4*zeta(28)_7^2 - 
    zeta(28)_4*zeta(28)_7 - zeta(28)_4, zeta(28)_4*zeta(28)_7^4 + 
    zeta(28)_4*zeta(28)_7^2 + zeta(28)_4*zeta(28)_7 + zeta(28)_4 )
*/

//G:=c9Group("4bl34p");
G := PermutationGroup(ATLASGroup("4bL34"));
M :=
GModule(G, [
    Matrix(K, 80, 80,
        [ [ 1/48, -5/96, 0, 1/96 ], [ -1/48, 1/32, 1/24, 1/96 ], [ 1/48, -5/96, 
        0, 1/96 ], [ -1/48, 5/96, 0, -1/96 ], [ -1/16, -23/96, -1/48, 5/96 ], [ 
        1/48, 3/32, -5/48, -7/96 ], [ 1/12, 7/48, 1/24, -1/16 ], [ -3/16, -5/96,
        5/48, 11/96 ], [ 1/8, -5/48, -1/6, -1/48 ], [ -1/8, -1/24, -1/24, 1/24 
        ], [ 1/4, 1/6, -5/24, -1/6 ], [ 1/16, 5/96, -5/48, -11/96 ], [ 1/8, 
        1/16, 0, -1/16 ], [ 1/8, 1/8, 0, 0 ], [ -1/8, 0, 0, 0 ], [ 0, 1/16, 
        -1/8, -1/16 ], [ 0, 1/8, 1/8, 0 ], [ 1/8, 1/8, -1/8, 0 ], [ -1/8, 1/16, 
        1/8, 1/16 ], [ 0, 1/8, 1/8, 0 ], [ 1/4, 3/16, -7/32, -5/32 ], [ -3/8, 
        -1/4, 1/32, 1/32 ], [ 1/8, 1/8, -5/32, -5/32 ], [ -1/16, 1/32, 1/32, 
        -1/16 ], [ -1/16, -5/32, -1/32, 1/16 ], [ 1/4, 1/16, -3/32, -1/32 ], [ 
        0, -1/16, -3/32, -1/32 ], [ -1/16, -1/32, 1/32, 0 ], [ 1/8, 3/16, 1/32, 
        -3/32 ], [ 3/16, 3/32, -1/32, -1/16 ], [ -3/8, -1/8, 7/32, 3/32 ], [ 0, 
        1/8, 1/32, -1/32 ], [ -7/16, -5/16, 1/8, 1/8 ], [ -1/8, 1/32, 3/16, 3/32
        ], [ -3/8, -7/32, 3/16, 3/32 ], [ 0, 1/16, 1/16, 0 ], [ 1/16, 5/32, 0, 
        -1/32 ], [ 1/8, 1/32, -1/16, -1/32 ], [ -1/8, -1/32, 1/16, 1/32 ], [ 0, 
        1/16, 1/16, 0 ], [ -1/8, -5/32, -1/16, 1/32 ], [ -1/16, -5/32, 0, 1/32 
        ], [ 5/16, 1/4, 0, -1/16 ], [ -1/4, -3/32, 1/16, -1/32 ], [ -3/16, 
        -1/32, 3/16, 3/32 ], [ 5/16, 9/32, -1/16, -3/32 ], [ 0, 1/16, 1/8, 1/16 
        ], [ -1/16, 1/32, 1/16, 1/32 ], [ 5/16, 9/32, -1/16, -3/32 ], [ 0, 0, 0,
        0 ], [ 5/16, 9/32, -1/16, -3/32 ], [ 3/16, 3/32, -1/16, -1/32 ], [ 
        -7/16, -7/32, 3/16, 5/32 ], [ -3/16, -5/32, 1/16, 3/32 ], [ 3/8, 1/4, 
        -1/8, -1/8 ], [ -1/4, -1/4, 1/8, 1/8 ], [ 13/32, 15/64, -1/4, -11/64 ], 
        [ -3/32, -15/64, -1/8, -1/64 ], [ 13/32, 11/64, -5/16, -11/64 ], [ -1/8,
        0, 1/32, -1/32 ], [ -1/8, -3/32, 3/32, 1/16 ], [ 1/32, 7/64, 0, -3/64 ],
        [ 11/32, 11/64, -3/16, -7/64 ], [ -1/8, -1/16, 1/32, 1/32 ], [ 5/32, 
        5/64, 0, -1/64 ], [ 3/16, 1/8, -3/32, -3/32 ], [ -15/32, -15/64, 3/16, 
        11/64 ], [ 1/32, 11/64, 0, -3/64 ], [ -3/32, -17/64, -3/32, 3/64 ], [ 
        -11/32, -11/64, 5/32, 9/64 ], [ -11/32, -17/64, 5/32, 11/64 ], [ -1/16, 
        -3/32, 0, 1/32 ], [ 1/16, 0, 0, 0 ], [ 1/32, 3/64, 1/32, -1/64 ], [ 
        -5/32, -13/64, 3/32, 7/64 ], [ -1/16, -3/32, 0, 1/32 ], [ 9/32, 9/64, 
        -5/32, -7/64 ], [ -1/4, -3/32, 1/16, 1/32 ], [ 1/32, 5/64, 1/32, 1/64 ],
        [ 9/32, 3/64, -5/32, -5/64 ], [ 5/48, 7/96, -1/24, -1/32 ], [ 1/16, 
        5/32, 0, -1/32 ], [ 5/48, 7/96, -1/24, -1/32 ], [ -5/48, -7/96, 1/24, 
        1/32 ], [ -7/24, 1/16, 5/24, 1/48 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 
        1/3, 0, -1/6, -1/24 ], [ 1/24, 1/16, 1/24, -1/48 ], [ 7/24, -1/16, 
        -5/24, -1/48 ], [ 1/3, 0, -1/6, -1/24 ], [ 1/24, 1/16, 1/24, -1/48 ], [ 
        0, 1/16, 0, -1/16 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 1/8, 1/8, 0, 0 ],
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        [ -5/16, -3/32, 3/32, 1/16 ], [ 5/16, 11/32, -1/32, -1/8 ], [ -1/16, 
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        ], [ -1/8, -3/16, -1/16, 0 ], [ 0, 1/16, 1/16, 0 ], [ 0, 1/16, 1/16, 0 
        ], [ -1/16, -9/32, -1/8, 1/32 ], [ 7/16, 9/32, -1/4, -5/32 ], [ -7/16, 
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        -5/16, -7/16, -1/32, 3/32 ], [ -1/4, -1/8, 3/32, 3/32 ], [ 5/16, 7/16, 
        1/32, -3/32 ], [ 0, -3/32, -1/32, 0 ], [ 0, -3/32, -1/32, 0 ], [ 1/2, 
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        -7/32 ], [ 1/8, 1/16, 1/32, 1/32 ], [ -1/16, -1/32, 1/16, 1/32 ], [ 0, 
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        ], [ 1/16, 1/32, -1/16, -1/32 ], [ 0, -3/32, -1/8, -1/32 ], [ -1/16, 
        -1/8, 1/16, 1/16 ], [ -1/16, -1/8, 1/16, 1/16 ], [ 1/16, 1/32, -1/8, 
        -3/32 ], [ 5/16, 7/32, -1/16, -3/32 ], [ -5/16, -7/32, 1/16, 3/32 ], [ 
        -1/16, -3/32, 0, 1/32 ], [ 1/48, -5/96, 0, 1/96 ], [ -1/48, 1/32, 1/24, 
        1/96 ], [ 1/48, -5/96, 0, 1/96 ], [ -1/48, 5/96, 0, -1/96 ], [ -3/16, 
        -11/96, 5/48, 5/96 ], [ 1/48, 1/32, 1/48, -1/96 ], [ -5/48, -19/96, 
        -1/48, 3/32 ], [ 3/16, 13/96, -7/48, -7/96 ], [ 1/16, 5/96, -5/48, 
        -11/96 ], [ 1/16, 23/96, 1/48, -5/96 ], [ -3/16, -5/96, 5/48, 11/96 ], [
        -1/16, -1/96, 7/48, 7/96 ], [ 1/8, 1/16, 0, -1/16 ], [ -1/8, -3/16, 0, 
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        ], [ -1/16, -5/32, 0, 1/32 ], [ 0, -1/16, -1/16, 0 ], [ -1/8, -1/32, 
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        ], [ 11/32, 11/64, -3/16, -7/64 ], [ -1/32, -7/64, 0, 3/64 ], [ -5/32, 
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        1/16, 0 ], [ -1/32, -5/32, 0, 0 ], [ 1/32, 0, 3/32, 1/16 ], [ -11/32, 
        7/64, 1/16, -3/64 ], [ -1/16, 9/64, 1/32, -5/64 ], [ -1/4, -9/32, 0, 
        3/32 ], [ -3/32, -1/8, 1/8, 3/32 ], [ 7/32, 1/8, -1/4, -3/32 ], [ 1/16, 
        -19/64, -1/16, 5/64 ], [ 0, 13/64, 0, -7/64 ], [ -1/16, 5/64, 1/16, 5/64
        ], [ 9/32, -1/64, -5/32, -1/64 ], [ 0, 3/32, -1/16, -3/32 ], [ -5/32, 0,
        3/32, 0 ], [ 7/32, 1/8, -3/32, -1/8 ], [ -5/32, -3/64, 5/32, 5/64 ], [ 
        -1/8, -7/64, 1/16, 5/64 ], [ 1/8, 3/32, 1/16, 1/32 ], [ 7/32, 3/16, 
        -1/32, -1/16 ], [ -7/32, -1/4, 1/32, 1/8 ], [ 1/16, 1/32, -1/24, 1/96 ],
        [ 1/48, -1/96, -1/48, 1/32 ], [ 5/48, -11/96, -1/24, 7/96 ], [ 1/16, 
        -5/96, -5/48, 1/32 ], [ -13/48, 1/12, 1/24, 0 ], [ 1/6, -5/96, -5/48, 
        1/32 ], [ -1/24, 1/32, 1/12, 5/96 ], [ 1/48, 1/24, -1/16, 1/48 ], [ 
        -1/6, 7/96, -1/24, -1/32 ], [ 1/6, 5/96, -3/16, 1/96 ], [ 1/24, -5/96, 
        -1/48, 1/32 ], [ 19/48, -1/24, -1/6, 0 ], [ -1/48, 13/96, 0, -5/96 ], [ 
        3/8, -1/8, -1/16, 1/16 ], [ 1/8, -1/8, -1/8, 1/16 ], [ -1/48, 3/32, 
        -1/12, -1/96 ], [ 7/48, 5/96, -1/16, -1/96 ], [ 1/3, -1/8, -1/6, 5/48 ],
        [ 1/16, -13/96, -1/48, 1/96 ], [ 1/4, -7/48, -5/48, 1/12 ], [ 5/16, 
        -1/32, -1/8, 1/32 ], [ -3/16, 5/32, 3/32, 0 ], [ -5/16, -1/16, 1/16, 
        -1/16 ], [ 3/16, -1/8, -5/32, 1/32 ], [ -3/16, -5/16, -1/32, 5/32 ], [ 
        1/16, -1/8, -1/8, 1/16 ], [ 5/16, 1/32, -5/32, 0 ], [ 5/16, 3/16, -3/32,
        -1/32 ], [ -1/16, 1/32, -1/16, -3/32 ], [ -1/16, -1/16, 3/32, 3/32 ], [ 
        1/16, 0, 1/32, -1/32 ], [ 1/8, -7/32, -3/32, 1/8 ], [ 1/16, -1/8, -1/16,
        1/16 ], [ 0, -1/16, 0, 0 ], [ 3/32, -3/64, 1/32, 5/64 ], [ 1/32, 1/64, 
        1/32, 1/64 ], [ 9/32, 11/64, -1/32, -1/64 ], [ -5/32, -1/64, 3/32, 3/64 
        ], [ -1/16, -7/32, -1/16, 3/32 ], [ -1/32, -11/64, -3/32, 1/64 ], [ 
        -3/16, -1/16, 1/8, 1/16 ], [ 7/32, 11/64, -5/32, -5/64 ], [ -3/32, 
        -1/64, 1/32, 3/64 ], [ -5/32, 17/64, 3/32, -3/64 ], [ 0, -3/32, 1/16, 
        3/32 ], [ -1/8, -5/32, 1/16, 1/32 ], [ 1/4, 3/32, -1/16, -1/32 ], [ 1/8,
        3/16, 0, 0 ], [ 0, 3/8, 0, -3/16 ], [ 0, 3/32, 1/16, -1/32 ], [ -3/8, 
        -3/32, 3/16, 3/32 ], [ -1/4, -1/8, 0, 1/16 ], [ 3/16, 1/16, 0, 0 ], [ 
        -1/4, 0, 0, -1/16 ], [ -1/8, 3/32, 1/16, -1/32 ], [ 3/16, 1/4, -1/16, 
        -1/16 ], [ -1/16, 0, 1/16, 0 ], [ -3/32, -9/64, 1/16, 5/64 ], [ -1/32, 
        0, -3/32, -1/16 ], [ -1/32, -5/32, 0, 0 ], [ -1/8, -25/64, -1/32, 9/64 
        ], [ 1/16, -5/64, -1/8, -1/64 ], [ 11/32, -7/64, -1/16, 3/64 ], [ 3/8, 
        11/64, -1/32, -3/64 ], [ 3/16, 1/8, -3/16, -1/8 ], [ -3/32, -1/8, 1/8, 
        3/32 ], [ 1/32, -1/32, 1/16, 0 ], [ -3/32, -9/32, 1/16, 1/16 ], [ 0, 
        3/32, -1/16, -3/32 ], [ 9/32, -1/64, -5/32, -1/64 ], [ -7/32, -1/8, 
        3/32, 1/8 ], [ -5/32, 0, 3/32, 0 ], [ 0, -3/64, 1/8, 5/64 ], [ 0, 
        -13/64, 0, 7/64 ], [ 5/32, 3/64, -5/32, -5/64 ], [ 1/16, -5/64, -1/16, 
        -5/64 ], [ -5/16, -3/16, 1/8, 1/8 ], [ 7/32, 3/16, -1/32, -1/16 ], [ 
        -3/32, -1/16, -1/32, 0 ], [ -9/32, -3/32, 7/32, 1/32 ], [ 3/16, -5/32, 
        -1/24, 7/96 ], [ -5/48, 3/32, 1/48, -7/96 ], [ -11/48, 5/32, 1/12, -1/32
        ], [ -1/16, 5/32, -1/48, -5/96 ], [ 1/6, 11/96, -1/12, -1/32 ], [ 11/48,
        3/16, -1/48, -1/12 ], [ -1/12, -5/96, 7/48, 1/32 ], [ 1/16, -5/16, 1/16,
        1/6 ], [ 13/48, -1/48, -5/48, 0 ], [ 3/16, 0, 0, 1/12 ], [ 7/24, 7/32, 
        -1/8, -5/96 ], [ 1/48, -1/16, 0, 1/48 ], [ 1/24, 5/48, -1/16, 1/24 ], [ 
        -5/16, -1/32, 3/16, -1/32 ], [ 1/8, -1/16, -1/16, -1/16 ], [ 1/24, 
        -3/16, 1/24, 1/48 ], [ 13/48, -7/96, -1/8, 5/96 ], [ -1/24, -3/16, 1/12,
        1/24 ], [ -5/16, -7/96, 5/48, 7/96 ], [ -1/16, 1/96, 1/12, -1/96 ], [ 
        1/4, 1/16, -3/32, -1/32 ], [ -1/16, 7/32, 0, -3/32 ], [ -1/8, -1/32, 
        7/32, 0 ], [ 1/2, 3/32, -3/32, -1/16 ], [ -1/4, -1/32, 3/32, 0 ], [ 
        -1/4, -5/32, 1/32, 1/16 ], [ 1/8, -1/8, -1/16, 0 ], [ -1/16, 0, 3/32, 
        -1/32 ], [ -5/16, 3/32, 1/32, -1/8 ], [ -1/16, 1/16, -3/32, -1/32 ], [ 
        -1/16, -1/16, 0, 1/16 ], [ 0, -3/32, 0, 1/32 ], [ 1/16, -1/16, -1/16, 0 
        ], [ -1/4, 1/32, 1/8, -1/32 ], [ 9/32, 5/64, -3/32, -7/64 ], [ 1/32, 
        -19/64, -7/32, 5/64 ], [ 1/32, 7/64, 1/32, -1/64 ], [ 7/32, 9/64, -1/32,
        -3/64 ], [ -1/4, -1/16, 1/16, 1/16 ], [ 3/32, -5/64, 1/32, -1/64 ], [ 
        -3/8, -1/8, 1/4, 1/16 ], [ -7/32, 11/64, 3/32, -1/64 ], [ -3/32, 11/64, 
        1/32, -1/64 ], [ 1/32, -5/64, -1/32, 3/64 ], [ -1/4, -3/32, 1/8, 1/32 ],
        [ 1/8, -3/32, 1/16, 3/32 ], [ 1/4, -5/32, -1/4, 1/32 ], [ -9/16, -5/32, 
        1/8, 3/32 ], [ 1/8, 1/16, -1/16, -1/16 ], [ 5/16, 3/16, -3/16, -1/8 ], [
        -3/16, 0, 1/16, 0 ], [ 1/16, 1/32, -1/16, -1/32 ], [ 1/8, 5/32, 1/16, 
        -1/32 ], [ 1/8, 1/16, 0, 0 ], [ -1/16, 0, 0, 0 ], [ 3/16, -1/16, -1/16, 
        0 ], [ 7/16, 0, -3/32, -1/32 ], [ 1/8, 3/32, -1/16, 1/32 ], [ -5/16, 
        3/64, 7/32, 1/64 ], [ 11/32, 9/32, 0, -1/8 ], [ -1/16, -9/64, -1/32, 
        5/64 ], [ -7/32, -3/32, 1/16, 0 ], [ 7/32, 1/64, -5/32, -3/64 ], [ 
        -1/32, 1/32, 0, 0 ], [ 3/32, 1/64, -3/16, -5/64 ], [ 0, -1/64, -3/32, 
        -3/64 ], [ -3/32, -5/32, 1/32, 1/32 ], [ 3/32, 0, -1/32, 0 ], [ -1/16, 
        0, 0, 0 ], [ -1/8, -5/32, -1/16, 1/32 ], [ -1/8, 15/64, 1/16, -5/64 ], [
        3/32, 1/16, -3/32, -1/8 ], [ -1/16, 5/64, 1/16, -3/64 ], [ -1/32, 1/32, 
        3/32, 1/32 ], [ -5/32, -15/64, 1/32, 5/64 ], [ 7/32, 0, -3/32, 1/16 ], [
        -5/32, -15/64, 1/32, 9/64 ], [ -1/8, -11/64, 1/8, 5/64 ], [ 3/32, 1/32, 
        -1/32, -1/32 ], [ -5/32, 3/32, 1/32, -1/32 ] ])    ,
    Matrix(SparseMatrix(K, 80, 80, [
    <1, 1, 1/2*(w^3 - w)>, 
    <2, 2, 1/2*(w^3 - w)>, 
    <3, 3, 1>, 
    <4, 4, -1>, 
    <5, 5, 1/2*(w^3 - w)>, 
    <6, 6, 1/2*(w^3 - w)>, 
    <7, 7, 1/2*(w^3 - w)>, 
    <8, 8, -1>, 
    <9, 9, 1/2*(w^3 - w)>, 
    <10, 10, -1>, 
    <11, 11, 1>, 
    <12, 12, 1>, 
    <13, 13, 1/2*(w^3 - w)>, 
    <14, 14, 1/2*(w^3 - w)>, 
    <15, 15, 1/2*(w^3 - w)>, 
    <16, 16, -1>, 
    <17, 17, 1/2*(w^3 - w)>, 
    <18, 18, -1>, 
    <19, 19, 1>, 
    <20, 20, 1>, 
    <21, 21, 1>, 
    <22, 22, -1>, 
    <23, 23, 1/2*(w^3 - w)>, 
    <24, 24, 1>, 
    <25, 25, 1/2*(-w^3 + w)>, 
    <26, 26, 1/2*(w^3 - w)>, 
    <27, 27, 1/2*(-w^3 + w)>, 
    <28, 28, 1/2*(-w^3 + w)>, 
    <29, 29, 1/2*(-w^3 + w)>, 
    <30, 30, -1>, 
    <31, 31, -1>, 
    <32, 32, 1>, 
    <33, 33, 1>, 
    <34, 34, -1>, 
    <35, 35, 1/2*(w^3 - w)>, 
    <36, 36, 1>, 
    <37, 37, 1/2*(-w^3 + w)>, 
    <38, 38, 1/2*(w^3 - w)>, 
    <39, 39, 1/2*(-w^3 + w)>, 
    <40, 40, 1/2*(-w^3 + w)>, 
    <41, 41, 1/2*(-w^3 + w)>, 
    <42, 42, -1>, 
    <43, 43, -1>, 
    <44, 44, 1>, 
    <45, 45, 1>, 
    <46, 46, -1>, 
    <47, 47, 1/2*(w^3 - w)>, 
    <48, 48, 1>, 
    <49, 49, 1/2*(-w^3 + w)>, 
    <50, 50, 1/2*(w^3 - w)>, 
    <51, 51, 1/2*(-w^3 + w)>, 
    <52, 52, 1/2*(-w^3 + w)>, 
    <53, 53, 1/2*(-w^3 + w)>, 
    <54, 54, -1>, 
    <55, 55, -1>, 
    <56, 56, 1>, 
    <57, 57, 1>, 
    <58, 58, -1>, 
    <59, 59, 1/2*(w^3 - w)>, 
    <60, 60, 1>, 
    <61, 61, 1/2*(-w^3 + w)>, 
    <62, 62, 1/2*(w^3 - w)>, 
    <63, 63, 1/2*(-w^3 + w)>, 
    <64, 64, 1/2*(-w^3 + w)>, 
    <65, 65, 1/2*(-w^3 + w)>, 
    <66, 66, -1>, 
    <67, 67, -1>, 
    <68, 68, 1>, 
    <69, 69, 1>, 
    <70, 70, -1>, 
    <71, 71, 1/2*(w^3 - w)>, 
    <72, 72, 1>, 
    <73, 73, 1/2*(-w^3 + w)>, 
    <74, 74, 1/2*(w^3 - w)>, 
    <75, 75, 1/2*(-w^3 + w)>, 
    <76, 76, 1/2*(-w^3 + w)>, 
    <77, 77, 1/2*(-w^3 + w)>, 
    <78, 78, -1>, 
    <79, 79, -1>, 
    <80, 80, 1>
    ]))
]: Check := false) where w := K.1 where K := ext<K|Polynomial(K, [4, 0, -3, 0, 1])> where K is 
RationalField();
K<w> := BaseRing(M);
K;
M;
